Subgroups — #14271285

Order 1856.

104 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂₉×#135	C₂	1	1	yes	maximal, characteristic
2	#11745310	C₂	1	2	yes	maximal, complemented
3	#11745185	C₂	1	2	yes	maximal, complemented
4	#11745167	C₂	1	1	yes	maximal, characteristic, complemented
5	#11745163	C₂	1	1	yes	maximal, characteristic, complemented
6	#41×C₂₉	C₂²	1	2	yes	—
7	Q₁₆×C₂₉	C₄	1	1	yes	characteristic, complemented
8	SD₁₆×C₂₉	C₄	1	2	yes	complemented
9	D₈×C₂₉	C₄	1	1	yes	characteristic, complemented
10	C₂×C₈×C₂₉	C₂²	1	1	yes	characteristic
11	C₄×Dic₂₉	C₂²	1	1	yes	characteristic
12	#90777	—	2	2	no	—
13	#90777	C₂²	1	2	yes	—
14	C₂×#6597	—	2	2	no	—
15	C₂×#6597	C₂²	1	1	yes	characteristic
16	Q₈×C₂₉	C₂×C₄	1	2	yes	—
17	D₄×C₂₉	—	2	2	no	—
18	D₄×C₂₉	C₂×C₄	1	2	yes	—
19	C₂×C₄×C₂₉	—	2	2	no	—
20	C₂×C₄×C₂₉	C₂³	1	1	yes	characteristic
21	C₂×Dic₂₉	—	2	1	no	—
22	C₈×C₂₉	C₂×C₄	1	1	yes	characteristic
23	C₈×C₂₉	C₂×C₄	1	1	yes	characteristic
24	#6597	—	2	2	no	—
25	#6597	D₄	1	2	yes	—
26	C₂²×C₂₉	—	2	2	no	—
27	C₂²×C₂₉	#41	1	1	yes	characteristic
28	C₄×C₂₉	—	2	2	no	—
29	C₄×C₂₉	C₂²×C₄	1	1	yes	characteristic
30	C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
31	Dic₂₉	—	4	1	no	—
32	#444	—	29	1	no	maximal, Sylow
33	C₂×C₂₉	—	2	1	no	—
34	C₂×C₂₉	—	4	2	no	—
35	C₂×C₂₉	C₄×D₄	1	1	yes	characteristic
36	#135	D₂₉	1	1	yes	characteristic
37	#131	—	29	2	no	—
38	#108	—	29	1	no	—
39	#104	—	29	2	no	—
40	#97	—	29	1	no	—
41	C₂₉	#444	1	1	yes	characteristic, complemented, Sylow
42	#41	C₂×D₂₉	1	2	yes	—
43	Q₁₆	Dic₂₉	1	1	yes	characteristic, complemented
44	SD₁₆	Dic₂₉	1	2	yes	complemented
45	D₈	Dic₂₉	1	1	yes	characteristic, complemented
46	M₁₆	—	29	2	no	—
47	M₁₆	—	58	2	no	—
48	C₂×C₈	—	29	1	no	—
49	C₂×C₈	—	58	2	no	—
50	C₂×C₈	C₂×D₂₉	1	1	yes	characteristic
51	C₄²	—	29	1	no	—
52	Q₈	C₂×Dic₂₉	1	2	yes	—
53	D₄	—	2	2	no	—
54	D₄	C₂×Dic₂₉	1	2	yes	—
55	C₂×C₄	—	2	2	no	—
56	C₂×C₄	—	58	1	no	—
57	C₂×C₄	C₂²×D₂₉	1	1	yes	characteristic
58	C₈	—	29	2	no	—
59	C₈	—	58	2	no	—
60	C₈	C₂×Dic₂₉	1	1	yes	characteristic
61	C₈	C₂×Dic₂₉	1	1	yes	characteristic
62	C₂²	—	2	2	no	—
63	C₂²	#90807	1	1	yes	characteristic
64	C₄	—	2	2	no	—
65	C₄	—	116	1	no	—
66	C₄	D₄×D₂₉	1	1	yes	characteristic
67	C₄	C₂²×Dic₂₉	1	1	yes	characteristic
68	C₂	—	2	1	no	—
69	C₂	—	4	2	no	—
70	C₂	D₄×Dic₂₉	1	1	yes	characteristic

	subgroup	G/H
center	C₄	D₄×D₂₉
commutator	C₄×C₂₉	C₂²×C₄
Frattini	C₂×C₄	C₂²×D₂₉
Fitting, prime radical	C₂₉×#135	C₂
socle	C₂×C₂₉	C₄×D₄
cosocle	C₂×C₄×C₂₉	C₂³
hypercenter	#135	D₂₉
hypocenter	C₂₉	#444
LCS	G ▷ C₄×C₂₉ ▷ C₂×C₂₉ ▷ C₂₉
UCS	C₁ ◁ C₄ ◁ C₂×C₄ ◁ #135

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
2. #11745310	C₂	semidirect
3. #11745185	C₂	semidirect
4. #11745167	C₂	semidirect
5. #11745163	C₂	semidirect
7. Q₁₆×C₂₉	C₄	semidirect
8. SD₁₆×C₂₉	C₄	semidirect
9. D₈×C₂₉	C₄	semidirect
41. C₂₉	#444	semidirect
43. Q₁₆	Dic₂₉	semidirect
44. SD₁₆	Dic₂₉	semidirect
45. D₈	Dic₂₉	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂₉×#135	2
#11745310	2
#11745185	2
#11745167	2
#11745163	2
#444	29